Find the absolute maximum and minimum values, and their locations, of the function f(x) in the given interval f(x) = x2−1, −1 ≤ x ≤ 2.
In the function, the highest value is considered the maximum value of a function, and the lowest value is considered the minimum value of the function.
Answer: The absolute maximum and minimum values of the given function are 3 and 0 respectively and they occur at x = 2 and x = -1, 1 respectively.
Let us see how to find absolute maximum and minimum
To find the absolute maximum and minimum, we will put the values of x in the given function.
The values of x as per the given interval are -1, 0, 1 and 2.
f(-1) = (-1)2 - 1 = 0
f(0) = 02 -1 = -1 and the absolute value is 1
f(1) = 12 -1 = 0
f(2) = 22 -1 = 3
Hence, from above we can see that the absolute minimum value of the function is 0 and it occurs at x = -1, 1 and the absolute maximum value is 3 and it occurs at x = 2.